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EN
This work presents a model of a temperature field in a steel element during multi-pass Gas Metal Arc Weld surfacing taking into account heat of the melted electrode material. An analytical solution for a half-infinite body model is obtained by aggregating temperature increments caused by applying liquid metal and heat radiation of a moving electrode. The assumptions are Gaussian distributed heat sources of applied melted electrode material and of an electric arc.
EN
In this work computations of a temperature field are carried out during multipass Gas Metal Arc Weld surfacing of a cuboidal steel element taking into account heat of the melted electrode material. The results are presented in the form of temporary and maximum temperature distribution in the element’s cross-section and thermal cycles at selected points.
EN
In this work, a model of a temperature field in a steel element during a singlepass arc weld surfacing is presented. Analytical solution for half-infinite body model is obtained by aggregating temperature increments caused by applying liquid metal and heat radiation of a moving electrode. The assumptions are Gaussian distributed heat sources of applied metal and the weld and of an electric arc heat source. Computations of the temperature field were carried out during arc weld surfacing of cuboidal steel element. The results are presented as temporary and maximum temperature distribution in the element’s crosssection and thermal cycles at selected points. The accuracy of the solution is verified comparing a calculated fusion line to that obtained experimentally.
4
Content available Didactic remarks on the power set
EN
The paper is devoted to correct understanding of the notation for the power set. Often this notation is mistaken with a power of the number 2. The correct definition of the power set is presented as well as several task which an serve for strengthening the understanding of this notion.
EN
Figurate numbers have simple geometric illustration: polygonal numbers can be represented by polygons, pyramidal numbers by pyramids, prismatic numbers by prisms, and trapezoidal numbers by trapezoids. The numbers mentioned above can be defined by formulae 1 or can be characterized by some arithmetic sequences of higher degrees which allow to obtain the corresponding formulae [3]. Figurate numbers due to their geometrical illustration and interesting properties can be of interest for school pupils.
6
Content available remote Development of pupil's mathematical thinking
EN
In this paper three types of exercises which develop mathematical reasoning and allow intuitive understanding of mathematical problems are presented. These exercises can be used during the lessons of mathematics.
8
Content available remote About definition of a periodic function
EN
In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.
9
Content available remote About definition of a periodic function
EN
In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.
10
Content available remote About Various Methods of Calculating the Sum [formula]
EN
Pupils of secondary school as well as students often have problems with calculating the sums of the mth powers of successive natural numbers. In this paper we present certain methods of finding such sums.
11
EN
Pupils and teachers often ask themselves a question: can induction definitions be replaced in an equivalent way by normal definitions? In this paper we present a method of replacement of induction definitions by normal definitions illustrating the given theorems by a few examples. From the viewpoint of the set theory operations and relations can be treated as certain sets. We discuss a method of replacement of an induction definition of the given set by a normal definition of this set. An induction definition of a set A has in general the following form (compare with [2]): D1. A set A is the least one from among the sets X satisfying the conditions: W1 (X) : a1,...,an ∈ X (the starting conditions), W 2 (X) : x1,...,xn ∈ X ⤇f (x1,...,xn) ∈ X (the induction conduction).
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